Write an equation of a Parabola with the given vertex and focus

Question

vertex (2,-3) ; focus (2,-2)

Answer 1

Hi Selina P.

Use the data given to calculate a, where is is the distance between the vertex and focus to give a, then plug than that into the vertex form of a parabola

Given

vertex (h, k) = (2, -3)

focus (2, -2)

x = 2 is the vertical axis of symmetry

Use the distance formula to find the distance between the vertex and focus

d = SQRT((x₂ - x₁)² + (y₂ - y₁)²)

a = ±1

f(x) = (x - 2)² - 3

f(x) = x² - 4x + 1

These two confirm the vertex and focus

You can graph both equations on a graphing calculator or at Desmos .con to confirm the vertex and focus.